Part 2: An Efficient Way to Compute the Largest Singular Values


16:00:00 - 18:00:00

R430 , Astronomy and Mathematics Building

To solve sparse symmetric and positive definite linear systems, Grigori, Nataf and Yousef proposed a preconditioning scheme in their recent paper entitled as \"Robust algebraic Schur complement preconditioners based on low rank corrections.” In the first part of this seminar, we will introduce this preconditioning scheme by focusing on (1) the proof that the condition number of the preconditioned system is bounded by a user defined value and (2) how the method can be parallelized. In the second part of this seminar, we will discuss a randomized method to compute the largest singular values and the corresponding singular vectors via power iteration and orthogonalization. The singular pairs will be applied in the preconditioning scheme.